Resumen de Some tests to count paradoxes of power indices

Josep Freixas Bosch , Xavier Molinero

• Within the context of weighted simple games we consider some well{known postulates for power indices. We essentially refer to the postulates: of donation, bloc and dominance; and to the power indices by: Banzhaf, Johnston, Deegan{ Packel and Holler. We do not consider the Shapley{Shubik index because it satis¯es all these three postulates.

  If a power index fails to satisfy one of the above postulates then the phe- nomena is regarded to be paradoxical. This work considers the paradoxes that arise from considering a particular postulate and a particular power index.

  The question that naturally appears for each pair (postulate / power index) is: how frequently does the paradox arise? By means of some theoretical methods we intend to partially answer the above question.